I think I would look at a self oscillating step-up transformer arrangement with a single rectifier or maybe a voltage doubler. Some feedback to the bias should be enough to stabilize the voltage if that is needed.
Consider that old CRT TV sets used to generate 12Kv - 15Kv from an oscillator and single power transistor.
I have not done the calculations but I doubt that you would get 10W of power at the output and if you did the voltage regulation would be extremely bad. betwixt suggestion is good use a step-up transformer and tripler to get the voltage and power you require. You could get an old CRT TV and get the transformer ,tripler and driver transistor from that.
Your load calculates as 1 mA and 10 MOhms. Here's an LC topology which might work (although I didn't build it in hardware). It doesn't require a jungle of diodes and capacitors, nor a transformer.
1) Op amp auto-detects resonant frequency of series LC.
2) Op amp changes state at proper times to drive the H-bridge.
3) As 24 VAC goes through the LC network, it's stepped up enormously.
4) Bridge voltage doubler is installed across capacitor. It generates 10 kV DC output to the load.
The step-up principle is the same as audio amplifier builders warn about when the output goes to a crossover consisting of a low-pass LC second-order. It must have a load attached. Because otherwise if a resonant note comes through the output, the voltage can soar to alarming levels.
Since your load is light, this concept might do the job. Real-life performance is hard to predict of course.